Details

Time bar (total: 16.4s)

sample34.0ms

Algorithm
intervals
Results
6.0ms265×body80nan
5.0ms45×body1280valid
5.0ms49×body640valid
3.0ms130×body80valid
2.0ms24×body320valid
0.0ms8×body160valid

simplify20.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize6.0ms

Local error

Found 1 expressions with local error:

2.2b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity sqrt-prod
4×difference-of-squares
3×distribute-lft-out-- add-log-exp
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out
Counts
1 → 19
Calls
1 calls:
70.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series105.0ms

Counts
1 → 3
Calls
1 calls:
105.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify644.0ms

Counts
22 → 22

prune55.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
20×sqrt-prod distribute-lft-out
18×times-frac
13×add-sqr-sqrt add-cube-cbrt
6×associate-/r*
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 55
Calls
2 calls:
44.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
44.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series211.0ms

Counts
2 → 6
Calls
2 calls:
62.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
149.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify462.0ms

Counts
61 → 61

prune130.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite353.0ms

Algorithm
rewrite-expression-head
Rules
742×*-un-lft-identity
700×sqrt-prod
594×times-frac
280×distribute-lft-out
254×add-sqr-sqrt
252×add-cube-cbrt
36×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
14×flip3-+ flip-+
12×div-inv
11×add-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv div-exp add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 445
Calls
4 calls:
65.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
42.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
47.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
130.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.0s

Counts
4 → 12
Calls
4 calls:
202.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
219.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
419.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
174.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify1.4s

Counts
457 → 457

prune964.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ 1 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.2b
(* (/ 1 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
0.2b
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
2340×sqrt-prod
1772×*-un-lft-identity
1731×times-frac
946×add-sqr-sqrt
671×add-cube-cbrt
612×distribute-lft-out
402×associate-*r*
70×unswap-sqr
68×sqrt-div
60×associate-/r/
54×add-exp-log
42×associate-*l*
39×associate-/l*
34×add-cbrt-cube
33×associate-/r*
30×flip3-+ flip-+ div-inv
24×div-exp
14×cbrt-undiv
12×prod-exp
9×pow1
6×cbrt-unprod
5×pow-flip
4×rec-exp sqrt-pow1 1-exp add-log-exp
3×frac-2neg clear-num
2×pow1/2
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative associate-/l/ inv-pow
Counts
4 → 1128
Calls
4 calls:
55.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
65.0ms
(/ 1 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
753.0ms
(* (/ 1 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
245.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series2.1s

Counts
4 → 12
Calls
4 calls:
503.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
558.0ms
(/ 1 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
251.0ms
(* (/ 1 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
807.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify2.0s

Counts
1140 → 1140

prune3.4s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes43.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify18.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
744.0ms8036×body80nan
327.0ms1734×body1280valid
214.0ms4056×body80valid
181.0ms1229×body640valid
59.0ms659×body320valid
20.0ms322×body160valid